Question

In how many ways can a group of 6 players be formed from 14 state level players and 8 district level players such that the group contains exactly 1 district level player?

Answer 1

Answer:

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A village has 10 players. A team of 6 players is to be formed. 5 members are chosen first out of these 10 players and then the captain from the remaining players. Then the total number of ways of choosing such teams is

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Solution

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Correct option is A)

A village has 10 players.

Now a team of 6 players is to be formed.

Thus 1

st

we select the 5 players from total 10 players in

10

C

5

ways and 6

th

person will select from the remaining 5 players in 5 ways.

Total number of ways =

10

C

5

×5=1260

Answer 2

Given:

Number of players that need to be in a group = 6

Number of state-level players = 14

Number of district-level players = 8

To find:

How many groups can be formed.

Solution:

If each group consists of 6 players and there should be exactly 1 district-level player in the team, then there must be 5 state-level players in the team.

If each team has 5 state-level players, then there can be only 2 teams possible as there are only 14 state-level players.

Thus 2 groups can be formed.